1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Coefficient of x^3

  1. May 15, 2008 #1
    Find the coefficient of x^3 in the expansion of (2x^2-3/x)^3


    I know how to do simple coefficients using pascalles triangle but I really don't know how to do this.
    Any help would be much appreciated.
     
  2. jcsd
  3. May 15, 2008 #2
    Write it as

    [tex](2x^2 - 3x^{-1})^3[/tex]

    From Pascal's triangle, you know how to expand

    [tex](a+b)^n[/tex]

    What can you replace with a and what can you replace with b?
     
  4. May 15, 2008 #3

    rock.freak667

    User Avatar
    Homework Helper

    [tex](2x^2-\frac{3}{x})^3[/tex]

    [tex] (\frac{1}{x}(2x^3-3))^3[/tex]

    How about now?
     
  5. May 15, 2008 #4
    Oh, that's a nice way of doing it :)
     
  6. May 15, 2008 #5

    rock.freak667

    User Avatar
    Homework Helper

    Usually (well for me), a binomial expansion is usually done with a variable and a constant.

    as for [itex](a+b)^n[/itex] is valid for [itex]|\frac{b}{a}|<1[/itex] But if a and b are variables, you'll have to do some fancy algebra to get the range for which it is valid.
     
  7. May 15, 2008 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Why is it only valid in some range??? I also don't see why you need to factor the original. (a+b)^3=a^3+3*a^2*b+3*a*b^2+b^3. Just put a=2x^2 and b=(-3/x), figure out which term is the x^3 term and evaluate it.
     
  8. May 15, 2008 #7

    rock.freak667

    User Avatar
    Homework Helper

    That's what I was taught.."validity of a binomial"
     
  9. May 15, 2008 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Got a reference? If you are thinking of the convergence of the infinite series for negative exponents, that is something to think about. But this is a positive exponent, the series is finite. There are no convergence issues.
     
  10. May 15, 2008 #9
    Besides, we're dealing with polynomials in the case of (a+b)^n
     
  11. May 15, 2008 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yeah, that's what I mean by finite series. You could also just forget about pascal's triangle and multiply it out. The power is only 3.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Coefficient of x^3
  1. X^4 - x^3 (Replies: 4)

  2. Inequality (-3/x) < 3 (Replies: 12)

Loading...